University of Groningen
Ab initio band structure calculations of Mg3N2 and MgSiN2
Fang, C.M.; Groot, R.A. de; Bruls, R.J.; Hintzen, H.T.; With, G. de
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Journal of Physics%3A Condensed Matter
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10.1088/0953-8984/11/25/304
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Fang, C. M., Groot, R. A. D., Bruls, R. J., Hintzen, H. T., & With, G. D. (1999). Ab initio band structure
calculations of Mg3N2 and MgSiN2. Journal of Physics%3A Condensed Matter, 11(25). DOI:
10.1088/0953-8984/11/25/304
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J. Phys.: Condens. Matter 11 (1999) 4833–4842. Printed in the UK
PII: S0953-8984(99)01113-3
Ab initio band structure calculations of Mg3 N2 and MgSiN2
C M Fang†, R A de Groot‡, R J Bruls†, H T Hintzen† and G de With†
†Laboratory of Solid State and Materials Chemistry, Eindhoven University of Technology,
Postbox 513, 5600 MB Eindhoven, The Netherlands
‡Electronic Structure of Materials, Research Institute for Materials, Toernooiveld 1,
6525 ED Nijmegen, The Netherlands
Received 21 January 1999
Abstract. Ab initio band structure calculations were performed for MgSiN2 and Mg3 N2 .
Calculations show that both nitrides are semiconductors with direct energy gaps at 0. The valence
bands are composed mainly of N 2p states hybridized with s and p characters of the metals. The
bottom of the conduction band consists of the s characters of Mg and N for Mg3 N2 , as well as
for MgSiN2 , while the characters of Si are higher in energy. The optical diffuse spectra show an
energy gap of about 2.8 eV for Mg3 N2 and 4.8 eV for MgSiN2 , in agreement with the calculated
values.
1. Introduction
In recent years nitrides have become an important subject of research [1, 2]. Some binary
nitrides, such as AlN and Si3 N4 , are used as high-performance engineering materials and
substrate materials in the semiconductor industry [1]. MgSiN2 is noted as an alternative ternary
compound for high temperature application, showing properties such as a reasonable thermal
conductivity, a rather good fracture toughness and hardness, and a good oxidation resistance up
to 920 ◦ C [3, 4]. MgSiN2 is also promising as a substrate material with an electrical resistivity
at room temperature comparable to and at high temperature higher than that of AlN [4]. Gaido
et al showed that (Eu-doped) MgSiN2 has not only similar luminescence properties to AlN,
but also a quantum yield for the green band as high as 40%, as compared to 8% for AlN [5].
MgSiN2 crystallizes in an orthorhombic structure, which is derived from the wurtzite
structure. The hexagonal structure is distorted because of the presence of two metal atoms and
displacement of the nitrogen atoms from the ideal positions in the wurtzite structure [6, 7].
The study for MgSiN2 has been concentrated on preparation, characterization [3, 4, 6–8],
mechanical and thermal properties [3, 4, 9], as well as the luminescence properties of the
rare earth doped materials [5, 10]. There has been almost no work performed for the electronic
properties, except the optical reflectance experiments, which showed MgSiN2 has an energy
gap of about 4.8 eV [5].
Mg3 N2 is widely used as a catalyst in the preparation of some nitrides, such as silicon
nitride ceramics and cubic boron nitride [11]. It was found in 1933 that some alkaline earth
metal nitrides M3 N2 (M = Be, Mg, Ca) have the anti-bixbyite structure [12–14]. Partin et al
for the first time refined fully the structure for Mg3 N2 from neutron time-of-flight diffraction
data [15]. In this structure the Mg atoms are at the tetrahedral sites of an approximately cubic
close packed array of N atoms (MgN4 ).
0953-8984/99/254833+10$19.50
© 1999 IOP Publishing Ltd
4833
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C M Fang et al
In this paper we report in detail the results of ab initio calculations for the electronic
structure of the ternary nitride MgSiN2 using the local spherical wave (LSW) approach. For
comparison calculations are also performed for the binary nitride Mg3 N2 . The bond valences
in the ternary nitrides are discussed. The electronic structure of the ternary nitride is compared
to those of the binary nitrides Mg3 N2 and Si3 N4 .
2. Structure and bond valences
MgSiN2 was first prepared by David and Lang using either (nitridation of) Mg2 Si and/or a
mixture of the binary nitrides [16]. Wintenberger et al refined the structure of MgSiN2 from
neutron and x-ray diffraction data [17]. For the purpose of our band structure calculations
the accurate structure of the compound was obtained from neutron diffraction data. MgSiN2
was prepared directly from the binary nitrides Mg3 N2 and Si3 N4 , as described in [3]. Neutron
diffraction determinations and refinements were performed at Intense Pulsed Neutron Source,
Argonne National Laboratory (US). The former structure [6, 16, 17] was confirmed. The
details of the preparation, structure determination and thermal expansion properties will be
published elsewhere [18]. MgSiN2 is orthorhombic, with lattice parameters: a = 5.2708 Å,
b = 6.4692 Å and c = 4.9840 Å. All the atoms are at general positions 4a of the space group
P na21 . Both Mg and Si atoms are tetrahedrally coordinated by N (see figure 1 and table 1).
The average Mg–N distance is 2.090 Å, which is shorter than that in Mg3 N2 (2.141 Å). The
Si–N distances range from 1.728 to 1.766 Å. The average Si–N distance is 1.752 Å, longer
than that in Si3 N4 (1.732 for β-Si3 N4 [19], 1.738 Å for α-Si3 N4 [20]). The Mg–Mg distances
are about 3.09 to 3.11 Å, which are also longer than those in Mg3 N2 , but shorter than those
(about 3.20 Å) in the Mg metal. The shortest N–N distance is about 2.829 Å, larger than that
in β-Si3 N4 (2.77 Å) [19].
Figure 1. The projection of the structure of MgSiN2 along [001].
Mg3 N2 and MgSiN2 ab initio band structure calculations
4835
Table 1. Interatomic distances (di , Å) and bond valences (V , vu) in the compounds Mg3 N2 and
MgSiN2 , and compared to that of β-Si3 N4 .
di (Å)
a. Mg3 N2 [15]
Mg–N(1) 2.145
–N(2) 2.084
–N(2) 2.160
–N(2) 2.179
b. MgSiN2 [18]
Mg–N(1) 2.0630
–N(1) 2.0707
–N(2) 2.1240
–N(2) 2.1019
Si–N(1) 1.7458
–N(1) 1.7284
–N(2) 1.7660
–N(2) 1.7657
c. β-Si3 N4 [19]
Si–N(1) 1.730
–N(1) 1.728
–N(2) 1.704
–N(2) 1.767
V (vu)
di (Å)
V (vu)
2.03
N(1)–Mg 2.145 (6×)
N(2)–Mg 2.084 (2×)
–Mg 2.160 (2×)
–Mg 2.179 (2×)
3.00
3.05
2.33
N(1)–Mg 2.0630
–Mg 2.0707
–Si 1.7458
–Si 1.7284
N(2)–Mg 2.1019
–Mg 2.1240
–Si 1.7657
–Si 1.7660
3.20
N(1)–Si 1.730 (3×)
N(2)–Si 1.728
–Si 1.704
–Si 1.767
3.00
2.98
3.78
3.98
2.91
The lattice parameter and coordinates of Mg3 N2 were obtained from the recent structure
determination by Partin et al [15]. Mg3 N2 is cubic with lattice parameter a = 9.9528 Å. The
metal (Mg) atoms are in general positions 48e of space group I a3 (x, y, z). There are two
crystallographically different kinds of N atom, as shown in tables 1 and 2. N1 is in positions
8b (1/4, 1/4, 1/4), and N2 in positions 24d (x, 0, 1/4). In the structure the N arrays are fairly
close to ideal cubic close packing. The 12 shortest N–N distances are in the range from 3.31
to 3.72 Å. Each nitrogen atom is coordinated by six Mg atoms. N1 has six Mg neighbours
with a distance of 2.145 Å, while N2 is coordinated by six Mg with different N–Mg distances
ranging from 2.084 to 2.179 Å. There are Mg–Mg distances of 2.72 Å.
In MgSiN2 both Mg and Si are in tetrahedral coordination by N, the same as Si in Si3 N4 .
The coordination of N by Mg and/or Si is different: N in Mg3 N2 has six nearest Mg neighbours,
and N in MgSiN2 is coordinated to four neighbours (two Mg and two Si), while in Si3 N4 every
N is coordinated to three tetrahedral Si [19, 20].
Some insight into the bonding of Mg and Si in MgSiN2 can be obtained using the concept
of bond valence [21]. The bond Vi is calculated from the relations: Vi = exp[(d0 − di )/b],
where di is the distance between the atoms of bond i, and b = 0.37 is the universal constant.
If the ionic model is used for Mg3 N2 and β-Si3 N4 , then d0 is 1.889 Å for Mg–N and 1.730 Å
for Si–N. The bond valence orPoxidation state V of an atom is calculated by summing over
all neighbouring atoms V =
Vi . The calculated bond valences are given in table 1. In
MgSiN2 , the bond valence of Mg is 2.33 valence units (vu), larger than 2.03 vu in Mg3 N2 ,
while Si have the valence of 3.78 vu, smaller than that in β-Si3 N4 . That is due to the fact that
Si is more electronegative than Mg.
3. Calculations and results
Ab initio band structure calculations were performed with the localized spherical wave
(LSW) method [22] using a scalar-relativistic Hamiltonian.
We used local-density
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C M Fang et al
Table 2. Input for the calculations (space group, lattice parameter, position and Wigner–Seitz
radius (RW S ) of atoms and empty spheres), and some calculated results (electronic configurations)
of Mg3 N2 [15] and MgSiN2 [18].
a. Mg3 N2 : space group I a3 (No 206), a = 9.9528 Å
Mg
N1
N2
Va1
Va2
Va3
Va4
WP
Coordinates
RW S (Å)
EC(N 2s)
EC(N 3s)
48e
8b
24d
8a
16c
24d
48e
(0.3890, 0.1520, 0.3823)
(1/4, 1/4, 1/4)
(0.9695, 0, 1/4)
(0, 0, 0)
(1/8, 1/8, 1/8)
(0.7394, 0, 1/4)
(0.2531, 0.1543, 0.6109)
1.101
1.363
1.342
1.363
1.220
1.148
0.536
[Ne]3s0.20 3p0.24 3d0.06
[He]2s1.82 2p4.45 3d0.02
[He]2s1.81 2p4.48 3d0.02
1s0.33 2p0.30 3d0.11
1s0.26 2p0.22 3d0.07
1s0.26 2p0.15 3d0.04
1s0.08 2p0.01 3d0.00
[Ne]3s0.19 3p0.23 3d0.05
([He]2s2 )3s0.03 2p4.38 3d0.02
([He]2s2 )3s0.03 2p4.40 3d0.02
1s0.34 2p0.28 3d0.09
1s0.26 2p0.19 3d0.05
1s0.27 2p0.15 3d0.03
1s0.07 2p0.01 3d0.00
b. MgSiN2 : space group P na21 (No 33), a = 5.2708, b = 6.4692 and c = 4.9840 Å [18]
Coordinates
Mg
Si
N1
N2
Va1
Va2
(0.0844, 0.6228, 0.9869)
(0.0694, 0.1242, 0.0000)
(0.0486, 0.0957, 0.3476)
(0.1087, 0.6552, 0.4102)
(0.8156, 0.6272, 0.7011)
(0.2618, 0.3767, 0.6389)
RW S (Å)
EC(N 2s)
EC(N 3s)
1.168
0.743
1.260
1.310
1.274
1.222
[Ne]3s0.20 3p0.27 3d0.13
[Ne]3s0.18 3p0.23 3d0.10
[Ne]3s0.17 3p0.17 3d0.02
([He]2s2 )3s0.03 2p4.66 3d0.03
([He]2s2 )3s0.04 2p4.73 3d0.04
1s0.32 2p0.37 3d0.19
1s0.29 2p0.30 3d0.14
[Ne]3s0.19 3p0.21 3d0.02
[He]2s1.77 2p4.69 3d0.04
[He]2s1.79 2p4.76 3d0.04
1s0.36 2p0.44 3d0.24
1s0.32 2p0.36 3d0.18
exchange–correlation potentials [23] inside space-filling, and therefore overlapping spheres
around the atomic constituents. The self-consistent calculations were carried out including
all core electrons. We performed iterations with about 245 k-points for Mg3 N2 and
1290 k-points for MgSiN2 distributed uniformly in an irreducible part of the Brillouin zone
(BZ), corresponding to a volume of the BZ per k-point of less than 1 × 10−6 Å−3 . Selfconsistency was assumed when the changes in the local partial charges in each atomic sphere
decreased to the order of 1 × 10−5 .
Recently it was found that in ionic compounds, such as alkali chlorides and alkaline earth
metal oxides, it is important to include the empty s states in a complete basis set [24–26]. It is
an interesting question to what extent the empty anion states influence the conduction bands in
nitrides, where the anionic 3s level is positioned higher in energy as compared with the oxides
and halides. In order to investigate this question two sets of calculations were performed:
one with N 2s states as valence states and one with N 3s states. In the construction of the
LSW basis [22, 27], the spherical waves were augmented by solutions of the scalar-relativistic
radial equations indicated by the atomic symbols 2p, 3s with 2s as core level for N, and 3s, 3p
for Mg and Si. The internal l summation used to augment a Hankel function at surrounding
atoms was extended to l = 2, resulting in the use of 3d orbitals for all the atoms. We also
performed calculations for the N without the N 3s states but N 2s in the basis set for the sake
of comparison, as mentioned before. Because the crystals are not very densely packed, it is
necessary to include empty spheres (Va) in the calculations. The functions 1s, 2p and 3d as an
extension were used for the empty spheres. The input parameters for calculations are listed in
table 2.
For a better understanding of the electronic structure of MgSiN2 , it is useful to compare
with the electronic structure of the binary nitrides Si3 N4 and Mg3 N2 . Si3 N4 has two
modifications (α and β) with the β-form the stable one at room temperature [19, 20]. Xu
and Ching performed band structure calculations for α- and β-Si3 N4 using the self-consistent
Mg3 N2 and MgSiN2 ab initio band structure calculations
4837
Table 3. Comparison of calculated electronic structure of Mg3 N2 , MgSiN2 and Si3 N4 . Data in
parentheses represent the calculated energy gaps with nitrogen 2s orbitals in the basis set.
Crystal
Mg3 N2
MgSiN2
Top of VB
Bottom of CB
Eg min (eV)
0, H
0
1.10(2.35)
0
0
4.35(6.45)
Eg (direct 0)
Width of VB (eV)
1.10(2.35)
4.40
4.35(6.45)
6.50
Position of N 2s
Experimental Eg (eV)
(−13.1 to −11.3)
2.8
(−15.5 to −12.3)
4.8
4.8 [5]
β-Si3 N4 [28, 29]
0–A
0
4.96 [28]
4.20 [29]
5.25 [28]
9.79 [28]
10.1 [29]
−18.2 to −14.0 [29]
4.6–5.5 [29]
α- Si3 N4 [28]
M
0
4.63
4.67
10.15
−18.4 to −14.3
Figure 2. BZ and high symmetry points of Mg3 N2 (a, left) and MgSiN2 (b, right).
orthogonalized linear combination of the atomic orbitals (OLCAO) method [28]. They found
that the electronic structures of α-Si3 N4 and β-Si3 N4 are similar, and their results for β-Si3 N4
are also in agreement with the calculations by Liu and Cohen using the first-principles pseudopotential total energy approach within a localized orbital formalism [29]. The main features
of the electronic structure of the nitrides are listed in table 3.
First calculated results for Mg3 N2 are presented. Figure 2(a) shows the Brillouin zone
(BZ) of Mg3 N2 . Some calculated results are given in tables 2 and 3. There are about 0.5
electrons in the sphere of Mg and about 6.3 electrons in the sphere of a nitrogen atom (table 2).
There are few electrons in the N 3s orbitals. We remark that not too much significance should
be attributed to differences in charge and orbital configurations, as these numbers are dependent
on the Wigner–Seitz radii, and the presence of empty spheres.
The partial and total densities of states (DOSs) and the energy bands along the highsymmetry directions in the BZ are shown in figures 3 and 4, respectively. The valence band
has a width of about 4.4 eV, and is composed mainly of N 2p. Other states have a density at
least one magnitude lower. However, there are characteristics of Mg 3s, 3p states in the valence
band, which indicates strong interactions between N 2p and Mg 3s, 3p states. The Mg 3s states
are mainly at the bottom of the valence band. The Mg 3p states are all over the valence band.
The calculations show that Mg3 N2 has a direct energy gap of 1.10 eV, as both the bottom of
the conduction band and the top of the valence band are at 0 point. The conduction band is
mainly composed of Mg 3s and N 3s states. The major part of the Mg 3p states lies about 3 eV
above the Fermi level.
4838
C M Fang et al
Figure 3. Partial and total density of states for Mg3 N2 . The Fermi level is at zero eV, the same as
in figures 5 and 6.
Figure 4. Dispersion of the energy bands for Mg3 N2 .
For the reason of comparison figure 5 shows the calculated partial and total DOS for
Mg3 N2 with N 2s as valence orbitals in the basis set. The N 2s band has a width of about
1.8 eV (from −13.1 to −11.3 eV). The 2s band of N1 has two features, with a single peak at
the upper part of the band, while the N2 2s band has three peaks in the upper part of the band.
Mg3 N2 and MgSiN2 ab initio band structure calculations
4839
Figure 5. Partial and total density of states of Mg3 N2 without N 3s states in the basis set.
That is mainly due to the N–Mg6 cluster with a single N–Mg distance for N1, but three different
N–Mg distances for N2, as shown in table 1. The influence from the N–N interactions may not
be important due to large N–N distances (3.31 to 3.72 Å). Figure 5 also shows a larger energy
gap, 2.35 eV. The bottom of the conduction band is mainly composed of Mg 3s characters.
The BZ for MgSiN2 is included in figure 2(b). Calculated electronic configurations are
given in table 2. The electronic configurations of Mg atoms are comparable to those in Mg3 N2 .
The N atoms in MgSiN2 have larger occupations in the 2p states, although they have smaller
spheres than those in the binary nitride Mg3 N2 (see table 2). Again, we remark that not too
much significance should be attributed to differences in charge and orbital configurations.
Figures 6 and 7 show the partial and total density of states, and the dispersion curve along the
high symmetry lines in the BZ of MgSiN2 , respectively.
Table 3 lists the major features of the electronic structures of the ternary nitride MgSiN2
and the binary nitrides Mg3 N2 and Si3 N4 . For MgSiN2 the bandwidth of the valence band,
which is composed mainly of the N 2p state hybridized with some Mg 3s, 3p and Si 3s, 3p
(figure 6), is about 6.50 eV, in between those of Mg3 N2 and Si3 N4 . The Mg 3s bands are all
over the valence band and are more delocalized as compared to that in Mg3 N2 . There is a
feature at about −4.0 eV, corresponding to the Mg 3s peak in the partial density of states in
Mg3 N2 (figures 3 and 5). There are Mg 3p states all over the valence band. The Si 3s and
3p states in the valence band are similar to that of Si3 N4 [28, 29]: a higher partial density of
the Si 3s states at the lower part of the band, while the partial density of the Si 3p states is
over all the band. The bandwidth of MgSiN2 is narrower than that of Si3 N4 . The energy gap
between the conduction band and the valence band is 4.35 eV. It is noted that the lower part
4840
C M Fang et al
Figure 6. Partial and total density of states of MgSiN2 .
Figure 7. Dispersion of the energy bands for MgSiN2 .
of the conduction band is mainly composed of N 3s and Mg 3s states. The main parts of the
Mg 3p and the Si 3s, 3p states are higher in energy. The dispersion curves of the energy bands
Mg3 N2 and MgSiN2 ab initio band structure calculations
4841
are very flat in the top of the valence band and sharp in the bottom of the conduction band.
These features indicate heavy holes and light conducting electrons. The dispersion curves also
show little anisotropy (figures 4 and 7).
Calculations with N 2s as valence orbitals in the basis set showed little changes for the
valence band. The N 2s band has a width of about 3.2 eV, in between that of Mg3 N2 (1.8 eV)
and Si3 N4 (about 4.1 eV). The N1 2s has a broader peak positioned at lower energy (about
−12.80 eV) than that of N2 s (at about −12.30 eV), which corresponds to the larger bond
valence (table 1). The calculations showed a larger energy gap (6.45 eV). Again, the bottom
of the conduction band consists mainly of Mg 3s states.
For both MgSiN2 and Mg3 N2 , there is little experimental data available. Optical diffusereflectance spectra were measured for Mg3 N2 and MgSiN2 by a Perkin–Elmer LS-50B
spectrometer in the range of 250–630 nm (2.0–5.0 eV). The scanning speed is 100 nm min−1 .
The splitting is 5 nm for excitation and 5 to 10 nm for emission, respectively. An energy gap
of about 2.8 eV is obtained for Mg3 N2 . The measured energy gap for MgSiN2 is 4.8 eV, in
agreement with the former measurements [5, 10]. This value is also in line with that of CaSiN2
(about 4.5 eV [30]). The calculated bandgaps (1.10 eV for Mg3 N2 , and 4.35 eV for MgSiN2 )
are smaller than the experimental values (2.8 eV and 4.8 eV, respectively). It is known that the
local density approximation employed in our calculations generally underestimates the energy
gaps for semiconductors [31]. The inclusion of the N 3s states as valence states is important.
Although the bandgap without them leads to a bandgap in closer agreement with experiment in
the case of Mg3 N2 , this agreement is fortuitous: a calculation better than LDA would produce
a much too large bandgap. This is best exemplified in the case of MgSiN2 , where the LDA
calculation without the N 3s states leads already to a gap 1.65 eV in excess in the experimental
value.
4. Conclusions
In conclusion, ab initio band structure calculations were performed for the binary nitride
Mg3 N2 and ternary nitride MgSiN2 . The calculations showed that both compounds are
semiconductors with a direct energy gap of 1.1 eV for Mg3 N2 and 4.35 eV for Mg3 SiN2 ,
in line with the experimental data (2.8 eV and 4.8 eV, respectively). In both compounds
the bottom of the conduction bands is mainly composed of Mg 3s and N 3s states, which is
important to understand the optical transition.
Acknowledgments
Mr P K de Boer (ESM KUN) is thanked for fruitful discussion about the electronic structure
for ionic materials, as well as results prior to publication. Mr J W H van Krevel and
Ms A C A Delsing (SVM, TUE) are acknowledged for help in the measurements of optical
diffuse reflectance spectra.
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